论文标题
小$ k $上的tuza常数$ c_k $的注释
A note on the Tuza constant $c_k$ for small $k$
论文作者
论文摘要
对于HyperGraph $ h $，横向是顶点的一个子集，其与每个边缘的相交是非空的。最小横向的基数是$ h $的横向数，以$τ（h）$表示。 tuza常数$ c_k $定义为$ \ sup {τ（h）/（m+n）} $，其中$ h $范围比所有$ k $ - 均匀的超graphs均分别为$ m $，$ m $和$ n $是边缘和角度的数量。我们在$ C_K $上给出上限和下限。上限以$ k \ geq 7 $改进已知的界限，下边界以$ k \ in \ {7，8，8，10，11，11，13，14，17 \} $改进已知的界限。
For a hypergraph $H$, the transversal is a subset of vertices whose intersection with every edge is nonempty. The cardinality of a minimum transversal is the transversal number of $H$, denoted by $τ(H)$. The Tuza constant $c_k$ is defined as $\sup{τ(H)/ (m+n)}$, where $H$ ranges over all $k$-uniform hypergraphs, with $m$ and $n$ being the number of edges and vertices, respectively. We give an upper bound and a lower bound on $c_k$. The upper bound improves the known ones for $k\geq 7$, and the lower bound improves the known ones for $k\in\{7, 8, 10, 11, 13, 14, 17\}$.
